Equation 677 Database

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Magma bc2f81d2670c…

magma bc2f81d2670c
Size
273
Isomorphism class hash
bc2f81d2670ccffca2d6cbc137b469ac294151d598b7d143b2ae675702d6bcad
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 272) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 01:22:07
Display reorder
68,66,67,71,69,70,63,64,65,62,60,61,254,12,51,73,228,13,52,74,229,14,53,72,230,15,50,76,231,16,48,77,232,17,49,75,233,18,57,79,234,19,58,80,235,20,59,78,236,21,56,82,237,22,54,83,238,23,55,81,239,266,260,259,265,40,199,223,168,41,200,224,169,39,198,222,170,36,202,226,171,37,203,227,172,38,201,225,173,46,197,221,174,47,195,219,175,45,196,220,176,42,193,217,177,43,194,218,178,44,192,216,179,258,264,263,257,186,204,142,90,187,205,143,91,188,206,141,92,189,207,138,93,190,208,139,94,191,209,140,95,184,210,133,88,185,211,134,89,183,212,132,87,180,213,136,84,181,214,137,85,182,215,135,86,261,271,272,262,28,164,126,243,29,162,127,244,27,163,128,245,24,167,129,242,25,165,130,240,26,166,131,241,34,159,124,247,35,160,125,248,33,161,123,249,30,158,120,250,31,156,121,246,32,157,122,251,267,270,269,268,155,4,117,101,153,5,118,99,154,3,119,100,151,1,116,97,152,0,114,98,150,2,115,96,146,8,108,107,144,9,109,105,145,7,110,106,149,6,111,103,147,11,112,104,148,10,113,102,256,255,253,252 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 273 = 13 + 5*52, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#299bf89dcaadd64e33422b05a87b398de7449d556bda64ba0ca787ebaa3d1bcb, M = {0, 5, 10, 16, 21, 26, 30, 35, 40, 46, 51, 56, 60} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 52): MacNeish's product over GF(4) x GF(13); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 21.

last edited by qawbecrdtey at 2026-10-08 01:22:08 · history